Stress Yield Criterion Research Articles

Magnetic resonance imaging based finite element modelling of the proximal femur: a short-term in vivo precision study

Proximal femoral fractures are a serious life-threatening injury with high morbidity and mortality. Magnetic resonance (MR) imaging has potential to non-invasively assess proximal femoral bone strength in vivo through usage of finite element (FE) modelling (a technique referred to as MR-FE). To precisely assess bone strength, knowledge of measurement error associated with different MR-FE outcomes is needed. The objective of this study was to characterize the short-term in vivo precision errors of MR-FE outcomes (e.g., stress, strain, failure loads) of the proximal femur for fall and stance loading configurations using 13 participants (5 males and 8 females; median age: 27 years, range: 21–68), each scanned 3 times. MR-FE models were generated, and mean von Mises stress and strain as well as principal stress and strain were calculated for 3 regions of interest. Similarly, we calculated the failure loads to cause 5% of contiguous elements to fail according to the von Mises yield, Brittle Coulomb-Mohr, normal principal, and Hoffman stress and strain criteria. Precision (root-mean squared coefficient of variation) of the MR-FE outcomes ranged from 3.3% to 11.8% for stress and strain-based mechanical outcomes, and 5.8% to 9.0% for failure loads. These results provide evidence that MR-FE outcomes are a promising non-invasive technique for monitoring femoral strength in vivo.

Smoothed particle hydrodynamics approach for modelling submerged granular flows and the induced water wave generation

In this study, we develop a Smoothed Particle Hydrodynamics (SPH) 2D-model for simulating fully submerged granular flows and their arising water waves. The granular particles are characterised by a non-Newtonian flow pattern, following a Casson constitutive law, generalised by applying the infinitesimal strain theory to avoid numerical singularities inherited from the original law. The implementation of this rheological model on the weakly compressible viscous Navier-Stokes equations enables the simultaneous modelling of the motion of granular flows and their resulting water waves, establishing a monolithic representation of fluid-structure coupling. The novelty of this model lies in the numerical continuity of the generalised rheological model based mainly on the yield stress criterion, which is computed purely from the mechanical properties of granular materials, including internal friction, cohesion, and viscosity coefficients. The proposed SPH model is validated through two benchmarks available in the literature, representing a submarine landslide along an inclined plane and an immersed granular column collapse. The outcomes of our study illustrate the effectiveness of the proposed model in accurately predicting the motions of submerged granular masses and their resulting water waves, which is crucial for accurately predicting the behaviour of underwater landslides and other natural hazards.

A Modified Design Stress Equation Based On Maximum Shear Stress Theory

The aim of this study was to formulate a new design stress equation for the analysis of two-dimensional plane elements using the maximum shear stress yield criterion known as the Tresca yield criterion. The existing Tresca yield equation was modified for a two-dimensional plane element to obtain a new general applied stress equation in terms of yield stress and stress factor. To get the specific applied stress equation for the twelve plate types considered, the polynomial shape parameters were solved to obtain the specific stress factor equation. To get the numerical value of the stress factor, a 1m by 1m mild steel of yield stress 250MPa, with deflection values taken at the point of maximum deflection, was analyzed. The numerical values of the stress factor for each plate type obtained were observed to be all less than unity, giving rise to a very high applied stress for plate types with no free edge and a moderately high stress for plate types with one free edge. This revealed the weakness of the existing yield criterion that may lead to failure. To improve this, a correction factor to take care of this limitation was introduced to the stress factor to have a factor of safety that will result in a design stress which is less than the yield stress of the material, by so doing ensuring safety. Therefore, the new design stress equation was found appropriate for predicting stress for the design of plane rectangular plates with one free edge, while this yield criterion is not advisable for use with plates without a free edge.
 

Punching Shear Failure Analysis of Reinforced Concrete Slabs under Close-in Explosion.

The susceptibility of reinforced concrete (RC) slabs to punching shear failure is heightened when subjected to close-in explosion loads, leading to a wider range of damage caused by the resultant leakage shock wave through the punching hole. Consequently, it is crucial to analyze the conditions for punching shear failure and the size of the punching hole in RC slabs. This study investigates the punching shear failure of RC slabs under close-in explosions through numerical simulation and theoretical analysis. Initially, a finite element model is developed to examine the distribution of the explosion load on the slab's surface. Subsequently, the critical explosion load for punching shear failure is determined using a damage criterion specific to RC slabs. Additionally, a calculation model based on the twin shear stress yield criterion is established to predict the punching hole's radius. To validate the accuracy of this method, a comparison is conducted with existing test results.

Exact solution of burst pressure for thick-walled pipes using the flow theory of plasticity

This paper develops an exact solution of burst pressure for defect-free, thick-walled pipes using the flow theory of plasticity in terms of the average shear stress yield criterion (or Zhu-Leis yield criterion). The pipe steel is assumed to obey the power-law strain hardening rule, and large plastic deformation is described by the finite strain theory. On this basis, internal pressure is obtained as a power series function of the effective strains on the inside and outside surfaces of the thick-walled pipe with use of the second Bernoulli numbers. At burst failure, the Zhu-Leis flow solution of burst pressure is determined as a power series solution, and the burst effective strains, the burst effective stresses, and the burst pressure are functions of the diameter ratio (Do / Di), strain hardening exponent (n), and ultimate tensile strength (UTS). Similarly, the Tresca and von Mises flow solutions of burst pressure are also determined as a power series solution in terms of the Tresca and von Mises yield criteria. A general closed-from exact solution of burst pressure is then proposed for the three yield criteria, and the results showed that the proposed exact solution matches well with the power series solution for each yield criterion. Moreover, the von Mises flow solution is an upper bound prediction, the Tresca flow solution is a lower bound prediction, and the Zhu-Leis flow solution is an intermediate prediction that agrees well with the finite element analysis results of burst pressure for thick-walled pipes. Two datasets of full-scale burst tests are then utilized to evaluate and validate the proposed flow solutions of burst pressure for both thin and thick-walled pipes.

Topology Optimization of fiber reinforced structures considering stress constraint and optimized penalization

The use of materials reinforced with fibers has been increasing due to their advantages, for example, the ratio between its mass and strength. For this reason, new additive manufacturing technologies have been developed for this material type. Some technologies allow tailoring fiber orientation, creating space for applying optimization techniques. On this account, many works dedicated to optimizing fiber orientation have been currently published. However, the critical issue of the stress yield criteria should be addressed. Thus, this work proposes to solve the Topology Optimization problem of minimizing the volume of the structure considering local stress constraints, determining the material distribution and the fiber orientation by using a proposed method named NDFO-adapt. The penalization used in the method is a field optimized together with the material distribution and the fiber angle. The same approach is extended to the penalization of SIMP and β parameters of threshold projection. This strategy enlarges the solution space and facilitates the discovery of previously unachievable local minima while eliminating the need for a heuristic selection of continuation methods. The Augmented Lagrangian method is used to deal with the local stress constraints. A mesh refinement scheme developed in the FEniCS project is proposed. Numerical examples are presented to illustrate the performance of the proposed method.

An Improved Anisotropic Non-associated Plastic Potential Based on Barlat’s Yld 2000-2D Yield Stress Criterion

An Improved Anisotropic Non-associated Plastic Potential Based on Barlat’s Yld 2000-2D Yield Stress Criterion

The contribution of Humboldt Glacier, northern Greenland, to sea-level rise through 2100 constrained by recent observations of speedup and retreat

Abstract. Humboldt Glacier, northern Greenland, has retreated and accelerated through the 21st century, raising concerns that it could be a significant contributor to future sea-level rise. We use a data-constrained ensemble of three-dimensional higher-order ice sheet model simulations to estimate the likely range of sea-level rise from the continued retreat of Humboldt Glacier. We first solve for basal traction using observed ice thickness, bed topography, and ice surface velocity from the year 2007 in a PDE-constrained (partial differential equation) optimization. Next, we impose calving rates to match mean observed retreat rates from winter 2007–2008 to winter 2017–2018 in a transient calibration of the exponent in the power-law basal friction relationship. We find that power-law exponents in the range of 1/7–1/5 – rather than the commonly used 1/3–1 – are necessary to reproduce the observed speedup over this period. We then tune an iceberg calving parameterization based on the von Mises stress yield criterion in another transient-calibration step to approximate both observed ice velocities and terminus position in 2017–2018. Finally, we use the range of basal friction relationship exponents and calving parameter values to generate the ensemble of model simulations from 2007–2100 under three climate forcing scenarios from CMIP5 (two RCP8.5 forcings, Representative Concentration Pathway) and CMIP6 (one SSP5-8.5 forcing, Shared Socioeconomic Pathway). Our simulations predict 5.2–8.7 mm of sea-level rise from Humboldt Glacier, significantly higher than a previous estimate (∼ 3.5 mm) and equivalent to a substantial fraction of the 40–140 mm predicted by ISMIP6 from the whole Greenland Ice Sheet. Our larger future sea-level rise prediction results from the transient calibration of our basal friction law to match the observed speedup, which requires a semi-plastic bed rheology. In many simulations, our model predicts the growth of a sizable ice shelf in the middle of the 21st century. Thus, atmospheric warming could lead to more retreat than predicted here if increased surface melt promotes hydrofracture of the ice shelf. Our data-constrained simulations of Humboldt Glacier underscore the sensitivity of model predictions of Greenland outlet glacier response to warming to choices of basal shear stress and iceberg calving parameterizations. Further, transient calibration of these parameterizations, which has not typically been performed, is necessary to reproduce observed behavior. Current estimates of future sea-level rise from the Greenland Ice Sheet could, therefore, contain significant biases.

Artificial neural network models of burst strength for thin-wall pipelines

Burst strength is critical to pipeline design, operation, and integrity management. The Barlow formula with the ultimate tensile stress (UTS) was often used to estimate burst strength of line pipes. To consider the plastic flow effect of pipeline steels, an average shear stress yield criterion was proposed, and the associated Zhu-Leis solution of burst strength was obtained for defect-free pipelines in term of UTS and strain hardening exponent, n, of materials. The Zhu-Leis solution was validated by more than 100 burst tests for various pipeline steels. The Zhu-Leis solution, when normalized by the Barlow strength, is a function of strain hardening rate, n, only. In contrast, experimental burst test data, when normalized by the Barlow strength, are a weak function of UTS and pipe diameter to thickness ratio D/t, in addition to be the function of n. Due to the difficulty of obtaining a closed-from solution using three-parameter regression, machine learning technology is adopted to develop alternative models of burst strength based on a large database of full-scale burst tests. In comparing to the regression, the machine learning method works well for both single and multiple parameters by introducing an artificial neural network (ANN), activation functions and learning algorithm for the network to learn from training data and then make predictions. Three ANN models were developed in this paper for predicting the burst strength of defect-free pipelines. Model 1 has one input variable and one hidden layer with three neurons; Model 2 has three input variables and one hidden layer with five neurons; and Model 3 has three input variables and two hidden layers with three neurons for the first hidden layer and two neurons for the second hidden layer. These three ANN models were then validated by the full-scale test data and evaluated through comparison with the Zhu-Leis solution and the linear regression results. On this basis, the best ANN model was recommended.

Analysis of the impact factor of burst capacity models for defect-free pipelines

The research on the failure pressure of perfect pipeline is the basis of evaluating the bearing capacity of defective pipeline. The applicability of impact factor of theoretical and empirical failure pressure prediction models for thin-walled pipes are evaluated with 77 full-scale burst test data. Impact factors analyzed in this study include diameter D, strain hardening exponent n, flow stress and yield criterion. The diameter D and strain hardening exponent n have less effect on the prediction of failure pressure of defect-free pipeline, while the flow stress and yield criterion have significant influence on the prediction of failure pressure. For the failure pressure assessment of defect-free pipelines, average shear stress yield (ASSY) criterion is the best applicable criterion, followed by Tresca and von Mises yield criterion. 1.0σu is the most accurate calculation method of flow stress for failure pressure of defect-free pipeline.

Estimation of Burst Pressure of PVC Pipe Using Average Shear Stress Yield Criterion: Experimental and Numerical Studies

Polyvinyl chloride (PVC) pipes have been extensively applied in water supply network fields. Understanding the mechanical properties and burst pressure of PVC pipes is necessary because a large number of pipes rupture due to excessive internal water pressure. In this paper, a practical approach based on the average shear stress yield (ASSY) criterion was proposed to assess the PVC pipe burst pressure. In addition, the PVC uniaxial tensile tests and the pipe burst tests were carried out to determine the material characteristic parameters and burst pressure of the PVC pipe. Furthermore, a finite element analysis (FEA) of PVC burst pressure was also performed based on the tangent intersection (TI) method to validate the proposed method and experimental results. Moreover, the impact of material parameters and pipe size, such as the strain hardening exponent and standard dimension ratio (SDR) on bursting pressure, were investigated. The comparison with the proposed theoretical model and the experimental and FEA results shows that the burst pressure derived from ASSY was consistent with the experimental data, with a relative error ranging from −2.76% to 2.65%, which is more accurate compared to other yield criteria. The burst pressure obtained by the ASSY approach declined with the increase of the hardening exponent n and increased with the increase of SDR. Therefore, the burst pressure solution-based ASSY proposed in this paper is an adequately suitable and precise predictive tool for assessing the failure pressure of PVC pipes.

Dynamic response and safety assessment of buried gas pipe subjected to ground surface explosion

Dynamic response of buried gas pipe subjected to the ground explosion is an important issue for the safety assessment of pipe. In this paper, the explosion tests of the full-scale model and 3D numerical models were employed to evaluate the dynamic response characteristics of the ground particles and the pipe. Meanwhile, parametric analysis was conducted to discuss the effects of different types of parameters for explosion source and pipe on the buried gas pipe's peak particle stress (PPS). Meanwhile, combined with the dynamic stress yield criterion of the pipe, the control standard of explosive charge under the action of the ground explosive load is obtained to prevent the damage of pipelines in different buried depths. The results showed that during third-party blasting operations, the internal pressure of the pipe should be reduced to better protect the pipe from damage, and attention should be paid to the velocity in the Y-direction of the pipe and the ground surface. Meanwhile, more attention should be paid to the safety protection of the buried pipe close to the interface between rock and soil.

Evaluate of anti-explosion for high-pressure gas steel pipeline subjected to ground explosion

One of the most significant current discussions in safety assessment about the buried high-pressure gas steel pipeline was the dynamic response of steel pipeline subjected to ground surface explosion, which played a key role in anti-explosion safety protection of steel pipeline engineering. In this paper, the typical burial conditions of gas steel pipeline in Chinese cities was selected as a case, and explosion tests of full-scale model with different scale explosive charge have been employed to verify the reliability of the 3D numerical model, specially, the strain hardening for the steel has been considered to increase the accuracy of the numerical model. Meanwhile, the parametric analysis was also conducted to discuss the effects of internal pressure of the steel pipeline, ground surface explosives charge, inner diameter of the steel pipeline, and the buried depth of the steel pipeline on the buried gas steel pipeline's peak particle stress (PPS). At last, combined with the dynamic stress yield criterion of the steel pipeline, the anti-explosion safety factor of the steel pipeline was fully discussed. The results showed that the decrease of internal pressure and the inner diameter of the steel pipeline can improve the anti-explosion performance of steel pipeline, and when the ground surface explosive charge was 10 kg, to prevent steel pipeline failure by ground surface blasting load, the inner diameter of steel pipeline should be less than 1 m, and the internal pressure of steel pipeline should not be greater than 2.0 MPa.

Through-wall yield ductile burst pressure of high-grade steel tube and casing with and without corroded defect

Service environment of tube and casing in deep and ultra-deep well is getting more and more complicated, and the internal pressure applied to tube and casing is higher, so that the high-grade steel tube and casing (HGTC) made of ductile material is widely used. Obviously, the calculation of ductile burst pressure for HGTC is one of the key factors in design and important to safe and efficient development of unconventional oil and gas resources. Here, based on the failure principle of through-wall yield and unified yield criterion, the unified formula of through-wall yield ductile burst pressure (TYBP) for tube and casing under practical service condition which can be used to calculate TYBP of API HGTC and non-API HGTC accurately and reasonably by using true material parameters, has been deduced in this paper with due consideration of the effect of Bauschinger effect (BE), material hardening and intermediate principal stress (IPS) on the TYBP, by which the influence rules of BE, IPS and yield criterion on TYBP of tube and casing have been investigated.（The effect of lattice effect (BE), material hardening and intermediate principal stress (IPS) on TYBP is accurately and reasonably derived from non-API HGTC by using real material parameters. The value of BE, IPS and the TYBP yield criterion of pipe and casing are studied. Eight kinds of classic through-wall yield ductile burst formulas for tube and casing made of new material have been be derived from a series of yield criterion, by which TYBP model of HGTC with and without corrosion defect has been established based on weighted twin shear stress yield criterion. The calculation results of TYBP model presented by this paper are the closest to the full-scale burst experimental data than the other burst models, which can provide an important reference for burst pressure design and estimation of HGTC in deep and ultra-deep well.

Mixed-integer second-order cone optimization for composite discrete ply-angle and thickness topology optimization problems

Discrete variable topology optimization problems are usually solved by using solid isotropic material with penalization (SIMP), genetic algorithms (GA), or mixed-integer nonlinear optimization (MINLO). In this paper, we propose formulating discrete ply-angle and thickness topology optimization problems as a mixed-integer second-order cone optimization (MISOCO) problem. Unlike SIMP and GA methods, MISOCO efficiently finds the problem’s globally optimal solution. Furthermore, in contrast with existing MISOCO formulations of discrete ply-angle optimization problems, our reformulations allow the structure to change topology, consider the more realistic Tsai–Wu stress yield criteria constraint, and eliminate checkerboard patterns using simple linear constraints. We address two types of discrete ply-angle and thickness problems: a structural mass minimization problem and a compliance optimization problem where the objective is to maximize the structural stiffness. For each element, one first chooses if the element is present or not in the structure. One can then choose the element’s ply-angle and thickness from a finite set of possibilities for the former case. The discrete design space for ply-angle and thickness is a result of manufacturing limitations. To improve the problem’s MISOCO solution approach, we develop valid inequality constraints to tighten the continuous relaxation of the MISOCO reformulation. We compare the performance of various MISOCO solvers: Gurobi, CPLEX, and MOSEK to solve the MISOCO reformulation. We also use BARON to solve the original MINLO formulations of the problems. Our results show that solving the MISOCO problem’s formulation using MOSEK is the most efficient solution approach.

Microstructural dependence of the incipient to homogeneous flow transition in metallic glass composites

As ductile derivatives of amorphous alloys, metallic glass composites balance high strength with the ability to mitigate catastrophic shear localization, which has long plagued monolithic metallic glasses. In this study, we employ a bonded-interface indentation technique coupled with strain field mapping to identify the governing yield criterion in metallic glass composites as a function of their microstructural length scales. A crossover from the shear plane to maximum shear stress yield criterion is uncovered at a crystalline fraction of approximately 60%, thus signaling an effective transition from incipient to homogeneous flow as the dominant deformation mode of the composite microstructure.

Solid expandable tubular forming behavior based on twin shear stress yield criterion: Analytical, numerical simulation and experiment

Abstract Solid Expandable Tubular (SET) technology is a recent important breakthrough in petroleum exploration and drilling. The expansion forming theory and the constitutive model of the tubular materials are the theoretical basis for the development of this technology. This work focuses on establishing analytical and finite element models on the basis of the Twin Shear Stress (TSS) yield criterion to investigate the forming behavior of solid expandable tubular. The expansion force expression of the power exponential hardening material model was derived. A constitutive model using the TSS yield criterion and related flow rules was proposed and implemented into the ABAQUS software. Further to this, variations of the expansion forces, residual stresses and plastic deformation under different expansion ratios and friction coefficients were investigated. In addition, a tubular expansion experiment was conducted to validate the analytical and finite element solutions. Results show that the expansion force expression is reliable, but there are discrepancies within a reasonable range. The finite element model is capable of predicting the expansion forces, residual stress distributions, thickness reduction and length shortening accurately. Moreover, it is found that the expansion ratio should be controlled below 35% to avoid burst and collapse of the expandable tubular in practical application. For expansion operations, suitable lubrication conditions should be determined to ensure an acceptable expansion force and maintain a certain friction coefficient.

Numerical study on failure process and ultimate state of steel bearing under combined load

The limit state and deformation performance of steel bearing under seismic load is one of the most critical points to consider the effective or rational design of bridge against strong ground motion. In the 2016 Kumamoto earthquake, various bridges are damaged by the earthquake. Among the components of the bridge, steel bearings are the most damaged part of the bridge, which affects the functionality of the entire bridge. Since the 1995 Southern Hyogo Prefecture Earthquake, several studies about the ultimate state of steel bearing during earthquake carried out. However, there are a few studies on analyzing the failure processes and ultimate state of steel bearing when various loads assumed at the time of the earthquake. Therefore, the study investigates the failure process and ultimate state of pin bearing and pin-roller bearing under combined load using static push-over analysis. First, the bridge axis and perpendicular bridge axis horizontal loading directions proposed depending on the actual earthquake directional behavior of the bridge. Then the analysis of each bearing conducted and clarified the failure process of each bearing that leads to failure based on the von mises stress yield criteria. Three-dimensional finite element method used to analyze the bearings. The analysis result found that set bolt and pin neck tensile failure were the probable failure mode of pin bearing, and failure mode of pin-roller bearing depends on vertical and horizontal loading direction. In the future, the result used to propose a new seismic resistance design and reinforcement method of bearings that satisfies the required performance.

Investigation on Welded T-Joint Distortion Using Virtual Manufacturing Tools with Simplified Procedure

This study presents a distortion analysis of a welded T-joint by using the virtual manufacturing (VM). Two different nonlinear 3D FEM-based VM systems, namely the general purpose MSC Marc/Mentat and the specialized Simufact.Welding software are compared and verified with the experiment. Both simulations are conducted based on an uncomplicated procedure without considering enormously on the weldment shape and resulting transient temperature distribution. Within this VM procedure, the heat source is modeled following Goldak’s double ellipsoid and the flow curve as one of the material properties of low carbon steel S235 is added with only one strain rate (0.001 s) based on non-linear isotropic plasticity model and von-Mises yield stress criterion. As the final outcome, the simplified procedures, weld geometry, and material properties will reduce the pre-processing without deteriorating the distortion results tremendously. Welding provides more structured and clearer simulation steps with more precise results of the angular distortion (Average of 7.25%) compared to the general purpose MSC Marc/Mentat (Average of 14.5%). This simplified simulation procedure without heat source and temperature calibration as well as complex material properties can be recommended for implementation if the time matter is constrained and the results are expected to be moderate.

Yield stress criteria to assess the buildability of 3D concrete printing

3D concrete printing (3DCP) using the extrusion method is a commonly used additive manufacturing technique to construct the structures layer by layer without using formwork. Therefore, the green (wet or fresh) strength of the printable concrete determines the possible printable height of the structure and the rate of printing to avoid collapse during the printing process. This paper aims to identify the buildability criteria based on the green strength of concrete and the effect of early age material properties on the stability of printed structures. The commonly available strength-based failure models based on the material yield stress and the vertical stresses induced were developed considering higher aspect ratios (height to width ratio). This may be not suitable for lower aspect ratios used in 3DCP layer geometries. Also, the frictional behaviour due to the applied vertical stresses should be considered in the material used for 3DCP applications. In this work, the Mohr-Coulomb based buildability criterion was developed and validated with laboratory experiments and numerical simulations. The laboratory experiments were carried out to establish the time-dependent material and rheological properties of 3D printable concrete mixes. Further, 3D printing of hollow circular sections was carried out to study the failure modes and to obtain the build height at the time of failure. The nonlinear finite difference model of the 3D printed sections was developed with the user-defined time-dependent material models to assess the accuracy of the proposed buildability criterion. Additionally, the proposed buildability criterion was further validated with the 3DCP experimental and numerical data presented in literature and all confirm that the proposed criterion shows higher accuracy over existing methods in assessing the buildability.